Notes on set theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1994
|
| Schriftenreihe: | Undergraduate texts in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 272 S. graph. Darst. |
| ISBN: | 0387941800 3540941800 |
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| 100 | 1 | |a Moschovakis, Yiannis N. |d 1938- |e Verfasser |0 (DE-588)112687776 |4 aut | |
| 245 | 1 | 0 | |a Notes on set theory |c Yiannis N. Moschovakis |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1994 | |
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Datensatz im Suchindex
| _version_ | 1804124053801271296 |
|---|---|
| adam_text | YIANNIS N
. MOSCHOVAKIS
NOTES ON SET THEORY
WITH 36 ILLUSTRATIONS
SPRINGER-VERLAG
NEW YORK BERLIN HEIDELBERG LONDON PARIS
TOKYO HONGKONG BARCELONA BUDAPEST
CONTENT
S
1
. INTRODUCTIO
N 1
PROBLEM
S FOR CHAPTE
R 1 5
2
. EQUINUMEROSIT
Y 7
COUNTABL
E UNION
S OF COUNTABL
E SET
S 9
TH
E REAL
S AR
E UNCOUNTABL
E 11
A
C
V(A) 15
SCHROEDER-BERNSTEI
N THEORE
M 16
PROBLEM
S FOR CHAPTE
R 2 18
3
. PARADOXE
S AN
D AXIOM
S 1
9
TH
E RUSSELL PARADO
X 21
AXIOMS (I
) - (VI
) 24
AXIOM
S FOR DEFINITE CONDITION
S AN
D OPERATIONS 27
CLASSES 28
PROBLEM
S FOR CHAPTE
R 3 31
4
. AR
E SET
S AL
L THER
E IS
? 3
3
ORDERE
D PAIR
S 35
DISJOINT UNIO
N 36
RELATION
S 37
EQUIVALENCE RELATION
S 38
FUNCTION
S 39
CARDINA
L NUMBER
S 43
STRUCTURE
D SET
S 45
PROBLEM
S FOR CHAPTE
R 4 46
XII NOTES ON SET THEORY
5
. TH
E NATURA
L NUMBER
S 5
3
EXISTENC
E OF TH
E NATURA
L NUMBER
S 54
UNIQUENESS OF TH
E NATURA
L NUMBER
S 54
RECURSION THEORE
M 55
ADDITIO
N AN
D MULTIPLICATIO
N 59
PIGEONHOLE PRINCIPL
E 64
STRING
S 67
TH
E CONTINUU
M 69
PROBLEM
S FOR CHAPTE
R 5 69
6
. FIXE
D POINT
S 7
3
POSET
S 73
PARTIA
L FUNCTIONS 76
INDUCTIV
E POSET
S 77
CONTINUOU
S LEAS
T FIXE
D POIN
T THEORE
M 79
ABOU
T TOPOLOG
Y 81
GRAPH
S 85
PROBLEM
S FOR CHAPTE
R 6 86
STREAM
S 87
SCOTT TOPOLOG
Y 91
DIRECTED-COMPLET
E POSET
S 91
7. WEL
L ORDERE
D SET
S 9
3
TRANSFINITE INDUCTIO
N 98
TRANSFINITE RECURSIO
N 100
ITERATIO
N LEMM
A 100
COMPARABILIT
Y OF WELL ORDERE
D SET
S 104
WELLFOUNDEDNESS OF
0
105
HARTOGS
THEORE
M 106
FIXE
D POIN
T THEORE
M 108
LEAST FIXE
D POIN
T THEORE
M 108
PROBLEM
S FOR CHAPTE
R 7 110
8
. CHOICE
S 11
7
AXIOM OF CHOICE 117
EQUIVALENT
S OF A
C 120
COUNTABL
E PRINCIPL
E OF CHOICE, AC^
R 122
AXIOM (VI
) OF DEPENDEN
T CHOICES, D
C 122
TH
E AXIOMATI
C THEORIE
S ZDC
, ZA
C 125
CONSISTENCY AN
D INDEPENDENC
E RESULT
S 126
PROBLEM
S FOR CHAPTE
R 8 127
CONTENTS XIII
9
. CHOICE
S CONSEQUENCE
S 13
1
TREES 132
KOENIG
S LEMM
A 133
FA
N THEORE
M 134
WELLFOUNDEDNESS OF
C
134
BES
T WELLORDERINGS 135
ABSORPTIO
N LAWS 138
KOENIG
S THEORE
M 140
COFINALITY, REGULAE
R CARDINAL
S 141
PROBLEM
S FOR CHAPTE
R 9 142
10
. BAIR
E SPAC
E 14
7
CARDINALIT
Y OF PERFECT POINTSET
S 150
CANTOR-BENDIXSO
N THEORE
M 151
PROPERT
Y P 152
ANALYTI
C POINTSET
S 153
PERFECT SET THEORE
M 157
BOREL SET
S 160
COUNTEREXAMPL
E T
O TH
E GENERA
L PROPERT
Y P 162
CONSISTENCY AN
D INDEPENDENC
E RESULT
S 164
PROBLEM
S FOR CHAPTE
R 10 165
BOREL ISOMORPHISMS 166
11
. REPLACEMEN
T AN
D OTHE
R AXIOM
S 16
9
REPLACEMEN
T AXIOM (VIII
) 170
TH
E AXIOMATI
C THEORIE
S ZFDC
, ZFA
C 170
GROUNDE
D RECURSIO
N THEORE
M 172
TRANSITIV
E CLASSES 174
BASIC CLOSURE LEMM
A 175
HEREDITARIL
Y FINITE SET
S 176
ZERMELO UNIVERSES 177
TH
E LEAST ZERMELO UNIVERSE 179
GROUNDE
D SET
S 180
PRINCIPL
E OF FOUNDATIO
N 180
TH
E AXIOMATI
C THEOR
Y ZERMELO-FRAENKEL, ZF
C 181
Z-F UNIVERSE
S 183
VON NEUMANN
S CLASS V 183
MOSTOWSKI COLLAPSING LEMM
A 183
CONSISTENCY AN
D INDEPENDENC
E RESULT
S 184
PROBLEM
S FOR CHAPTE
R 11 185
XIV NOTES ON SET THEORY
12
. ORDINA
L NUMBER
S 18
9
CHARACTERIZATIO
N OF TH
E ORDINA
L ASSIGNMEN
T 193
CHARACTERIZATIO
N OF TH
E ORDINAL
S 194
ORDINA
L RECURSIO
N 197
ORDINA
L ADDITION
, MULTIPLICATIO
N 197
VON NEUMAN
N CARDINAL
S 198
TH
E OPERATION X
A
200
TH
E CUMULATIV
E RAN
K HIERARCH
Y 201
PROBLEM
S FOR CHAPTE
R 12 203
TH
E OPERATION 3
Q
205
STRONGLY INACCESSIBLE CARDINAL
S 206
FREGE CARDINAL
S 206
QUOTIENT
S OF EQUIVALENCE CONDITION
S 207
A
. TH
E REA
L NUMBER
S 20
9
CONGRUENCE
S 209
FIELD
S 211
ORDERE
D FIELDS 212
UNIQUENES
S OF TH
E RATIONAL
S 214
EXISTENC
E OF TH
E RATIONAL
S 215
COUNTABLE
, DENSE
, LINEA
R ORDERING
S 219
TH
E ARCHIMEDEA
N PROPERT
Y 221
NESTE
D INTERVA
L PROPERT
Y 226
DEDEKIN
D CUT
S 229
EXISTENC
E OF TH
E REA
L NUMBER
S 231
UNIQUENESS OF TH
E REA
L NUMBER
S 234
PROBLEM
S FOR APPENDI
X A 236
B
. AXIOM
S AN
D UNIVERSE
S 23
9
SET UNIVERSES 242
PROPOSITION
S AN
D RELATIVIZATION
S 243
RIEGER UNIVERSES 248
RIEGER
S THEORE
M 248
ANTIFOUNDATIO
N PRINCIPLE
, AF
A 254
BISIMULATION
S 255
TH
E ANTIFOUNDE
D UNIVERSE 259
ACZEL S THEORE
M 259
PROBLEM
S FOR APPENDI
X B 262
INDE
X 26
7
|
| any_adam_object | 1 |
| author | Moschovakis, Yiannis N. 1938- |
| author_GND | (DE-588)112687776 |
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| callnumber-subject | QA - Mathematics |
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| dewey-full | 511.3/2220 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/22 20 |
| dewey-search | 511.3/22 20 |
| dewey-sort | 3511.3 222 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| isbn | 0387941800 3540941800 |
| language | English |
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| spelling | Moschovakis, Yiannis N. 1938- Verfasser (DE-588)112687776 aut Notes on set theory Yiannis N. Moschovakis New York [u.a.] Springer 1994 XIV, 272 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in mathematics Axiomatische Mengenlehre Zahlentheorie Set theory Mengenlehre (DE-588)4074715-3 gnd rswk-swf Mengenlehre (DE-588)4074715-3 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006420340&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moschovakis, Yiannis N. 1938- Notes on set theory Axiomatische Mengenlehre Zahlentheorie Set theory Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4074715-3 |
| title | Notes on set theory |
| title_auth | Notes on set theory |
| title_exact_search | Notes on set theory |
| title_full | Notes on set theory Yiannis N. Moschovakis |
| title_fullStr | Notes on set theory Yiannis N. Moschovakis |
| title_full_unstemmed | Notes on set theory Yiannis N. Moschovakis |
| title_short | Notes on set theory |
| title_sort | notes on set theory |
| topic | Axiomatische Mengenlehre Zahlentheorie Set theory Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Axiomatische Mengenlehre Zahlentheorie Set theory Mengenlehre |
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